Let's go through the problems shown in the image:

PART 4: Absolute Value

1. Evaluate the following absolute value expressions:

• a. |5 − 8| $|5 − 8| = |-3| = 3$
• b. |12 + (−4)| $|12 + (−4)| = |12 − 4| = |8| = 8$
• c. |−7| + |3| $|-7| + |3| = 7 + 3 = 10$
• d. |10 − 15| + |3 − 7| $|10 − 15| + |3 − 7| = |-5| + |-4| = 5 + 4 = 9$
• e. |−25 + 10| $|-25 + 10| = |-15| = 15$

2. Simplify and evaluate these combinations of absolute values:

• a. |2| + |−6| − |4 − 9| $|2| + |-6| − |4 − 9| = 2 + 6 − |-5| = 2 + 6 − 5 = 3$
• b. |7 − 13| + |20 − 15| $|7 − 13| + |20 − 15| = |-6| + |5| = 6 + 5 = 11$
• c. |18 − 25| + |(−3) + 4| $|18 − 25| + |-3 + 4| = |-7| + |1| = 7 + 1 = 8$
• d. |−15 + 6| + |9 − 5| $|-15 + 6| + |9 − 5| = |-9| + |4| = 9 + 4 = 13$
• e. |25 − 30| + |−10| $|25 − 30| + |-10| = |-5| + 10 = 5 + 10 = 15$

PART 5: Radicals

1. Simplify the following square roots:

• a. $\sqrt{50}$ $\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$
• b. $\sqrt{72}$ $\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}$
• c. $\sqrt{32}$ $\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}$
• d. $\sqrt{75}$ $\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$

2. Add or subtract the radicals:

• a. $3\sqrt{2} + 5\sqrt{2}$ $3\sqrt{2} + 5\sqrt{2} = (3 + 5)\sqrt{2} = 8\sqrt{2}$
• b. $4\sqrt{3} − \sqrt{3}$ $4\sqrt{3} − \sqrt{3} = (4 − 1)\sqrt{3} = 3\sqrt{3}$
• c. $\sqrt{18} + 2\sqrt{2}$ $\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$ So, $3\sqrt{2} + 2\sqrt{2} = (3 + 2)\sqrt{2} = 5\sqrt{2}$
• d. $5\sqrt{7} − 2\sqrt{7}$ $5\sqrt{7} − 2\sqrt{7} = (5 − 2)\sqrt{7} = 3\sqrt{7}$

Do you need further clarifications or any additional details?

Here are five related questions for practice:

1. What is the absolute value of $|-16|$?
2. Simplify $\sqrt{200}$.
3. How would you add $\sqrt{18} + \sqrt{50}$?
4. What is the result of $|3 - 9| + |12 - 20|$?
5. Simplify $\sqrt{45} + \sqrt{80}$.

Tip: When adding or subtracting radicals, make sure the radicals have the same root value (like terms) to combine them easily.